Channel-Adapted Quantum Error Correction for the Amplitude Damping Channel

Error correction procedures are considered which are designed specifically for the amplitude damping channel. Amplitude damping errors are analyzed in the stabilizer formalism. This analysis allows a generalization of the [4,1] ldquoapproximaterdquo amplitude damping code. This generalization is presented as a class of [2(M+1),M] codes; quantum circuits for encoding and recovery operations are presented. A [7,3] amplitude damping code based on the classical Hamming code is presented. All of these are stabilizer codes whose encoding and recovery operations can be completely described with Clifford group operations. Finally, optimization options are described in which recovery operations may be further adapted according to the damping probability gamma.